Electromagnetic Probe

ABSTRACT

An electromagnetic probe  1  measures the electromagnetic properties of a sub surface formation GF in a limited zone surrounding a well-bore hole WBH. The well-bore hole is filled with a well-bore fluid DM. The probe comprises a pad  2  having a first face defining a first area arranged to be positioned in contact with a well-bore wall WBW. The probe  1  further comprises: at least two transmitting antennas  4 A,  4 B defining a central point CP between them, each antenna being spaced from a distance do from the central point, and at least a first  5 A,  5 B and a second set  5 C,  5 D of receiving antennas, each set comprising a first receiving antenna  5 A;  5 C and a second receiving antenna  5 B;  5 D, the first receiving antenna being positioned on one side of the transmitting antennas and the second receiving antenna being positioned on other side of the transmitting antennas so that each set encompass the transmitting antennas  4 A,  4 B.

FIELD OF THE INVENTION

The invention relates to an electromagnetic probe for measuring theelectromagnetic properties of a subsurface formation in a limited zonesurrounding a bore hole. Another aspect of the invention relates to alogging tool comprises such a probe for performing logs of subsurfaceformation bore hole.

A further aspect of the invention relates to a method for measuring theelectromagnetic properties of a subsurface formation in a limited zonesurrounding a bore hole.

A particular application of the probe, the logging tool and the methodaccording to the invention relates to the oilfield services industry.

BACKGROUND OF THE INVENTION

Logging devices which measure formation dielectric constant are known,for example from U.S. Pat. No. 3,849,721 and U.S. Pat. No. 3,944,910.The logging device includes a transmitter and spaced receivers mountedin a pad that is urged against a bore hole wall. An electromagneticmicrowave is transmitted into the formations, and the wave which haspropagated through the formations is received at the receiving antennas.The phase shift and attenuation of this wave propagating in theformations is determined from the receivers output signals. Thedielectric constant and the conductivity of the formations can then beobtained from the phase shift and attenuation measurements. Twotransmitters are generally used in a bore hole compensated array tominimize the effect of bore hole rugosity, tool tilt, anddissimilarities in the transmitters, receivers, and their electroniccircuits.

SUMMARY OF THE INVENTION

One goal of the invention is to propose an electromagnetic probe and/ormethod for measuring the electromagnetic properties of a subsurfaceformation in a limited zone surrounding a bore hole with a betteraccuracy than prior art device and/or method.

According to the invention, it is proposed an electromagnetic probe forperforming electromagnetic measurements of the formation dielectricproperties according to different wave polarization, at differentinvestigation depths within the formation (radial depths) and atdifferent frequencies.

The electromagnetic probe is intended to measure the dielectricpermittivity and electric conductivity of geological formationsurrounding the bore hole. The measurements are differentialmeasurements based on phase shift and amplitude attenuation ofelectromagnetic waves between two transmitting antennas towards at leasttwo receiving antennas encompassing the transmitting antennas. Under thecontrol of an electronic arrangement, emitting antennas are excited andreception signals at receiving antennas are measured. The attenuationand phase shift measured between the two emitting antennas gives theapparent wave vector known as k, which is directly linked to thepermittivity and conductivity of the formation. However, thismeasurement is affected by the presence of an eventual mudcake on thewell-bore wall and fluid mixture (drilling fluid) into the formation.This uncertainty is resolved by performing additional measurements, eachmeasuring an additional phase shift and an additional attenuation.

A first set of additional measurements are performed with differentpolarizations, one according to a broadside mode and one according to anendfire mode. A second set of additional measurements are performed withvarious depths of investigation. A third set of additional measurementis performed in order to determine the dielectric properties of themudcake and the fluid mixture. These additional measurements provide aset of coherent and complementary data enabling to determine the mudcakethickness, and permittivity and conductivity of the fluid mixture, themudcake and the formation at different radial depths and at differentfrequencies.

More precisely, a first aspect of the present invention relates to anelectromagnetic probe for measuring the electromagnetic properties of asubsurface formation in a limited zone surrounding a well-bore hole, thewell-bore hole being filled with a well-bore fluid. The probe comprisesa pad having a first face defining a first area arranged to bepositioned in contact with a well-bore wall. The probe furthercomprises:

-   at least two transmitting antennas defining a central point between    them,-   at least a first and a second set of receiving antennas, each set    comprising a first receiving antenna and a second receiving antenna,    the first receiving antenna being positioned on one side of the    transmitting antennas and the second receiving antenna being    positioned on other side of the transmitting antennas so that each    set encompass the transmitting antennas,-   the first set of receiving antennas is spaced from a first distance    from the central point, the second set of receiving antennas is    spaced from a second distance from the central point, the second    distance being greater than the first distance,-   the transmitting and receiving antennas are positioned along a line    in the first face,-   an electronic arrangement comprising at least one transmitter module    arranged to excite the transmitting antennas by applying an    excitation signal according to at least a first and a second    frequency, and at least one receiver module coupled to at least one    receiving antenna and arranged to determine an attenuation and a    phase shift of each reception signal provided by each receiving    antenna relatively to the excitation signal.

The transmitting antennas of the probe are sensibly identical, eachantenna comprising two perpendicular dipoles embedded in a cavity andarranged to transmit electromagnetic energy according to a broadsidemode and an endfire mode. The receiving antennas of the probe aresensibly identical, each antenna comprising two perpendicular dipolesembedded in a cavity and arranged to receive electromagnetic energyaccording to a broadside mode and an endfire mode.

According to another aspect of the invention, the probe furthercomprises a first open-ended coaxial wire arranged in the first side andpositioned sensibly perpendicularly to the first area between atransmitting antenna and a receiving antenna.

According to still another aspect of the invention, the pad furthercomprises a second face arranged to be in contact with the well-borefluid, and the probe further comprises a second open-ended coaxial wirearranged in the second face.

According to a further aspect of the invention, the electronicarrangement comprises a first open ended coaxial wire controllingcircuit, said circuit comprising:

-   a transmitting module for sending a high-frequency input signal into    the first open ended coaxial wire, and-   a receiving module for determining a first reflection coefficient    based on a high frequency output signal reflected at the aperture of    the first open-ended coaxial wire and a propagation coefficient    based on a high frequency output signal received by the first    open-ended coaxial wire following an excitation of the transmitting    antennas. The electronic arrangement may further comprise a second    open ended coaxial wire controlling circuit, said circuit    comprising:-   a transmitting module for sending a high-frequency input signal into    the second open ended coaxial wire, and-   a receiving module for determining a second reflection coefficient    based on a high frequency output signal reflected at the aperture of    the second open-ended coaxial wire.

Advantageously, the electronic arrangement of the electromagnetic probeof the invention has a homodyne architecture comprising a variable highfrequency source providing a high frequency signal to:

-   the at least one transmitter module arranged to excite the    transmitting antennas,-   the at least one receiver module coupled to the at least one    receiving antenna, and-   the transmitting module and the receiving module of the first and    second open ended coaxial wire controlling circuits.

Another aspect of the present invention relates to a logging toolarranged to be deployed in a well-bore hole, wherein the logging toolcomprises an electromagnetic probe according to the invention and apositioning arrangement for positioning the probe in contact with awell-bore wall at a determined depth.

Still another aspect of the present invention relates to a method formeasuring the electromagnetic properties of a subsurface formation in alimited zone surrounding a well-bore hole, the well-bore hole beingfilled with a well-bore fluid.

The method comprises the steps of:

-   a) positioning the probe according to the invention at a first    depth,-   b) transmitting an excitation electromagnetic energy around a    central point into the limited zone by energizing the first    transmitting antenna with an excitation signal according to a    broadside mode and according to a first frequency,-   c) measuring a broadside/broadside reception signal at the receiving    antennas according to a broadside mode and measuring simultaneously    a broadside/endfire reception signal at the receiving antennas    according to an endfire mode, at least at a first distance and at a    second distance from the central point,-   d) repeating the transmitting step b) and the measuring steps c) by    energizing the second transmitting antenna with an excitation signal    according to a broadside mode and according to a first frequency,-   e) transmitting an excitation electromagnetic energy around a    central point into the limited zone by energizing the transmitting    antennas with an excitation signal according to an endfire mode and    according to the first frequency,-   f) measuring an endfire/ endfire reception signal at the receiving    antennas according to the broadside mode and measuring    simultaneously an endfire/broadside reception signal at the    receiving antennas according to the endfire mode at least at the    first distance and at a second distance from the central point,-   g) repeating the transmitting step e) and the measuring steps f) by    energizing the second transmitting antenna with an excitation signal    according to an endfire mode and according to a first frequency, and-   h) repeating the steps b) to g) at least at a second frequency.

Optionally, the transmitting steps b), d), e) and g) may be performedsimultaneously, the excitation electromagnetic energy transmitted by thefirst transmitting antennas being signed by a first low frequency, theexcitation electromagnetic energy transmitted by the second transmittingantennas being signed by a second low frequency.

Optionally, the transmitting steps b) to h) may be performedsimultaneously, the excitation signal comprising a plurality offrequencies, at least the first and the second frequencies.

According to another aspect of the invention, the method furthercomprises the steps of:

-   determining an attenuation and a phase shift of each reception    signal provided by each receiving antenna relatively to the    excitation signal,-   estimating the electromagnetic properties of the subsurface    formation in the limited zone surrounding the well-bore hole for at    least a first radial investigation depth correlated to the first    distance and a second radial investigation depth correlated to the    second distance.

According to another aspect of the invention, the method furthercomprises the steps of:

-   measuring a high frequency output signal received by a first    open-ended coaxial wire following an excitation of the transmitting    antennas,-   determining an attenuation of the high frequency output signal    relatively to the excitation signal, and-   estimating a thickness of a mudcake on the well-bore wall by    determining a transmission coefficient based on the attenuation and    phase shift.

According to still another aspect of the invention, the method furthercomprises the steps of:

-   measuring a high frequency output signal received by the receiving    antennas following an excitation of a first open-ended coaxial wire,-   determining an attenuation and a phase shift of the high frequency    output signal relatively to the excitation signal, and-   estimating a thickness of a mudcake on the well-bore wall by    determining a propagation coefficient based on the attenuation.

According to still another aspect of the invention, the method furthercomprises the steps of:

-   sending a high-frequency input signal into a first open ended    coaxial wire in contact with the well-bore wall,-   measuring a high frequency output signal reflected by the mudcake    via the first open-ended coaxial wire,-   estimating the electromagnetic properties of the mudcake on the    well-bore wall by determining a mudcake reflection coefficient based    on the high frequency output signal.

According to still another aspect of the invention, the method furthercomprises the steps of:

-   sending a high-frequency input signal into a second open ended    coaxial wire in contact with a well-bore fluid,-   measuring a high frequency output signal reflected by the second    open-ended coaxial wire,-   estimating the electromagnetic properties of the well-bore fluid by    determining a well-bore fluid reflection coefficient based on the    high frequency output signal.

According to still another aspect of the invention, the method furthercomprises the step of comparing the signals provided by the first openended coaxial wire and the second open ended coaxial wire for estimatingthe quality of the pad application against the bore-hole wall.

According to another aspect of the invention, the method furthercomprises the steps of correcting the calculated electromagneticproperties of the subsurface formation in the limited zone surroundingthe well-bore hole based on the estimated electromagnetic properties andthe thickness of the mudcake. This correction yields the radial profileelectromagnetic properties of the geological formation free of mudcakeeffects.

The electromagnetic probe of the invention enables a higher measurementaccuracy than the electromagnetic propagation tool as described in theprior art. With the method of the invention, it is possible to estimatethe electromagnetic properties in a radial profile away from thewell-bore wall and/or at different frequencies.

The electromagnetic probe according to the invention enables to reduceuncertainties during interpretation of petrophysical data. Theelectromagnetic probe measurements are based on high frequencyelectromagnetic waves interaction with water molecules in the matrixpores of the geological formation. These measurements yield informationon fluids occupying the matrix pores, on the matrix itself, the fluid tomatrix interaction and on the geological structure of the formation.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of examples and not limitedto the accompanying figures, in which like references indicate similarelements:

FIG. 1.A schematically illustrates a typical onshore hydrocarbon welllocation;

FIG. 1.B schematically illustrates a top view of a bore hole in ageological formation;

FIGS. 2.A, 2.B, 2.C schematically show a cross-section view, a bore holewall contacting side view and a bore hole fluid contacting side view ofa probe for measuring the electromagnetic properties of a subsurfaceformation according to the invention, respectively;

FIG. 3.A schematically shows in greater details a cross-section view ina cross dipole antenna of the probe according to the invention;

FIGS. 3.B and 3.C schematically illustrate the cross dipole antenna ofFIG. 3.A in an endfire mode and in a broadside mode, respectively;

FIGS. 4 and 5 schematically show a transmitting circuit and a receivingcircuit of an electronic arrangement of the probe according to theinvention, respectively;

FIG. 6 schematically shows an open ended coaxial wire controllingcircuit of the electronic arrangement of the probe according to theinvention;

FIGS. 7.A and 7.B show a typical envelope of the radial depthsensitivity response measured by the receiving antennas according to theendfire mode and the broadside mode, respectively; and

FIGS. 8.A and 8.B show typical permittivity and conductivity dispersioncurves relatively to the frequency, respectively.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1.A schematically shows a typical onshore hydrocarbon well locationand surface equipments SE above a hydrocarbon geological formation GFafter drilling operation has been carried out. At this stage, i.e.before a casing string is run and before cementing operations arecarried out, the well-bore is a bore hole WBH filled with a fluidmixture DM. The fluid mixture DM is typically a mixture of drillingfluid and drilling mud. In this example, the surface equipments SEcomprises an oil rig OR and a surface unit SU for deploying a loggingtool TL in the well-bore WB. The surface unit may be a vehicle coupledto the logging tool by a line LN. Further, the surface unit comprises anappropriate device for determining the depth position of the loggingtool relatively to the surface level. The logging tool TL may comprise acentralizer. The centralizer comprises a plurality of mechanical armthat can be deployed radially for contacting the well-bore wall WBW. Themechanical arm insures a correct positioning of the logging tool alongthe central axis of the well-bore hole. The logging tool TL comprisesvarious sensors and provides various measurement data related to thehydrocarbon geological formation GF and/or the fluid mixture DM. Thesemeasurement data are collected by the logging tool TL and transmitted tothe surface unit SU. The surface unit SU comprises appropriateelectronic and software arrangements for processing, analyzing andstoring the measurement data provided by the logging tool TL.

The logging tool TL comprises a probe 1 for measuring theelectromagnetic properties of a subsurface formation according to theinvention. Once the logging tool is positioned at a desired depth, theprobe 1 can be deployed from the logging tool TL against the bore holewall WBW by an appropriate deploying arrangement, for example an arm.

FIG. 1.B is a top cross-section view in a geological formation GF. Thebore hole WBH is filled with the fluid mixture DM, generally drillingfluid and drilling mud. The bore hole wall screens the particles of mudsuspended into the fluid mixture. Thus, a shallow layer of mud, theso-called mudcake MC is generally formed on the bore hole wall WBW. Aflushed or invaded zone IZ forming a first concentric volume surroundsthe bore hole WBH. The fluid mixture DM generally filtrates through themudcake MC and penetrates into the formation, forming the invaded zoneIZ. The radial depth of the invaded zone varies from a few inch to a fewfeet. A true or virgin zone VZ surrounds the invaded zone IZ. It is onlyfilled with the natural geological formation fluid. A further transitionzone may be present between the invaded zone IZ and the virgin zone VZ.

Therefore, the measurement performed by the logging tool TL are affectedby the presence of the fluid mixture DM into the geological formationGF, by the size of the invaded zone IZ and by the presence and size ofthe mudcake MC.

FIGS. 2.A, 2.B and 2.C show the electromagnetic probe 1 according to across section, a bore hole wall contacting face and a bore hole fluidcontacting face views, respectively.

The electromagnetic probe 1 comprises a pad 2. The pad is a conductivemetal housing, for example made in a metallic material like stainlesssteel. The pad 2 has a first face defining a first area arranged to bepositioned in contact with a bore hole wall WBW. The other faces of thepad are arranged to be in contact with the fluid mixture DM present inthe bore hole WBH.

The pad 2 is coupled to the tool TL by an arm AR (partially shown). Thearm AR enables the deployment of the electromagnetic probe 1, moreprecisely the pad 2, from the tool TL into the bore hole WBH. Inparticular, a first face of the pad 2 is deployed against the bore holewall WBW while a second face of the pad 2 is in contact with the borehole fluid DM. In this example, the bore hole wall WBW consists in theformation GF covered by the mudcake MC.

The electromagnetic probe 1 comprises an electronic arrangement 3, twotransmitting antennas 4A and 4B, and eight receiving antennas 5A, 5B,5C, 5D, 5E, 5F, 5G and 5H. The transmitting antennas 4A and 4B and thereceiving antennas 5A, 5B, 5C, 5D, 5E, 5F, 5G and 5H are positioned inthe pad along a line AA′ in the first face arranged to be positioned incontact with the bore hole wall WBW.

The two transmitting antennas 4A and 4B define a central point CPbetween them. Each antenna is spaced from a distance do from the centralpoint CP. The distance do sensibly defines the electromagnetic probevertical resolution, for example 1 inch. The transmitting antennas 4Aand 4B are connected to the electronic arrangement 3. The eightreceiving antennas 5A, 5B, 5C, 5D, 5E, 5F, 5G and 5H are groupedaccording to four sets, each set comprising two receiving antennas. Eachreceiving antenna of the set is positioned on each side of thetransmitting antennas. Thus, each set of receiving antennas encompassthe transmitting antennas.

The first set of receiving antennas comprises the first receivingantenna 5A and the second receiving antenna 5B. The first set ofreceiving antennas is spaced from a first distance d₁ from the centralpoint CP.

The second set of receiving antennas comprises the third receivingantenna 5C and the fourth receiving antenna 5D. The second set ofreceiving antennas is spaced from a second distance d₂ from the centralpoint CP. The second distance d₂ is greater than the first distance d₁.

The third set of receiving antennas comprises the fifth receivingantenna 5E and the sixth receiving antenna 5F. The third set ofreceiving antennas is spaced from a third distance d₃ from the centralpoint CP. The third distance d₃ is greater than the second distance d₂.

The fourth set of receiving antennas comprises the seventh receivingantenna 5G and the height receiving antenna 5H. The fourth set ofreceiving antennas is spaced from a fourth distance d₄ from the centralpoint CP. The fourth distance d₄ is greater than the third distance d₃.

The receiving antennas 5A, 5B, 5C, 5D, 5E, 5F, 5G and 5H are connectedto the electronic arrangement 3.

The measurements provided by each receiving antenna correspond todifferent radial depths in the geological formation GF. The first set ofreceiving antennas spaced from the first distance d₁ from the centralpoint CP enables to investigate the geological formation at a firstradial depth RD₁. The second set of receiving antennas spaced from thesecond distance d₂ from the central point CP enables to investigate thegeological formation at a second radial depth RD₂. The third set ofreceiving antennas spaced from the third distance d₃ from the centralpoint CP enables to investigate the geological formation at a thirdradial depth RD₃. The fourth set of receiving antennas spaced from thefourth distance d₄ from the central point CP enables to investigate thegeological formation at a fourth radial depth RD₄.

The maximum distance between the emitting antennas and the mostly spacedset of receiving antennas is limited by dissipation effect. Thisdistance is typically several inches.

Additionally, the electromagnetic probe 1 comprises a first 6A and asecond 6B open-ended coaxial wire. Each open-ended coaxial wirecomprises an inner conductor made of a metallic material and an outerconductor shell made of an insulating material. Each open-ended coaxialwire is secured in a hole of the metallic pad. The first open-endedcoaxial wire 6A is arranged in the first side and positioned sensiblyperpendicularly to the first area between a transmitting antenna and areceiving antenna, for example between the transmitting antenna 4A andthe receiving antenna 5B (others positions between a transmittingantenna and any receiving antenna are possible). The first open-endedcoaxial wire 6A is connected to a first open ended coaxial wirecontrolling circuit of the electronic arrangement 3. The secondopen-ended coaxial wire 6B is arranged in the second face of the pad incontact with the well-bore fluid DM. The position of the secondopen-ended coaxial wire 6B within the pad is not important provided thatit is in contact with the well-bore fluid. Any pad face may beconvenient except the one in contact with the bore hole wall. The secondopen-ended coaxial wire 6B is connected to a second open ended coaxialwire controlling circuit of the electronic arrangement 3.

Further, the electromagnetic probe 1 comprises a well-bore fluid (e.g.mud) temperature sensor 7, for example a thermistance. The temperaturesensor 7 is connected to the electronic arrangement 3.

Further, the electromagnetic probe 1 may comprise accelerometers, e.g.three axis accelerometers (not shown). The accelerometers are embeddedin the pad in order to reference electromagnetic probe to a positioningtool within the logging tool.

One or more coaxial cables (not shown) may be run though the arm AR forconnecting the electronic arrangement 3 with the tool TL. The tool TLcontains the bulk of the down-hole electronics and provides energy andcontrol commands, and gathers measurements from the electromagneticprobe 1.

Alternatively, the electronic arrangement 3 may comprise a signalgeneration, acquisition, processing and data communication module (notshown) for directly transmitting measurements to the surface equipmentand receiving control commands from it.

FIGS. 3.A to 3.C show a transmitting antenna 4A or any of the receivingantennas. The transmitting antenna 4A is a cross-dipole antenna that canbe energized to produce electromagnetic wave having a magnetic dipolecharacteristic. Advantageously, the transmitting antenna is a puremagnetic point dipole. In the example of FIGS. 3, the antenna 4Acomprises a square aperture or cavity 42 in a metal body 41, for examplestainless steel. The metal body 41 is inserted in an appropriate hole ofthe pad 2. Metallic antenna elements 44, 46 cross the cavity fromdifferent opposing sides. They are positioned within the cavity so as tonot touch where they cross. The cavity 42 is filled with any nonconductive material. The cavity 41 may be sealed by a window 43,preferably in a material that does not perturbate high frequency wavepropagation. A first end of the metallic antenna elements is coupled toan associated transmitting module of the electronic arrangement by aconductor wire 45. A second end of the metallic antenna is connected tothe metal body 41. The conductor wire 45 is insulated for passagethrough the metal body 41.

This antenna is advantageous because it is adapted to measure properlytwo perpendicular modes with high accuracy due to the low cross-talkbetween the two magnetic dipoles.

The other transmitting antenna 4B is similarly constructed.

The transmitting antenna operates as follows. The cross-dipole antennacan be used to produce electromagnetic wave with a controlled magneticdipole direction. When a current is applied to an antenna element,particular oscillation modes are excited in the cavity. Preferably, thedominant mode is the transverse electric TE₁₀ (evanescent mode). Thus,the transmitting antenna is sensibly a magnetic point dipole in a widefrequency range (e.g. from 10 MHz to 2 GHz) and in every down-holemedia. FIGS. 3.B and 3.C schematically show a vertical antenna element44 parallel to the longitudinal axis AA′ of the logging tool and ahorizontal antenna element 46 perpendicular to the longitudinal axisAA′, respectively. FIG. 3.B shows an antenna operating in an endfiremode, namely energizing of the horizontal antenna element 44(cross-section shown) results in a vertical magnetic moment (asindicated by the vertical arrow EFM). FIG. 3.C shows an antennaoperating in a broadside mode, namely energizing of the vertical antennaelement 46 (cross-section shown) results in a horizontal magnetic moment(as indicated by the horizontal arrow BSM). The receiving antennas 5A,5B, 5C, 5D, 5E, 5F, 5G and 5H may be of similar construction to that ofthe transmitting antennas 4A and 4B shown in FIGS. 3.A to 3.C. They arecoupled to receiving modules of the electronic arrangement. Thereceiving antennas are excited by the transmitted electromagnetic wavecomponent parallel to the receiving antenna magnetic dipole. Thehorizontal element provides an endfire signal when excited by a verticalmagnetic dipole, while the vertical element provides a broadside signalwhen excited by a horizontal magnetic dipole.

An endfire signal excited by a horizontal magnetic dipole or a broadsidesignal excited by a vertical magnetic dipole are the signature ofanisotropy or inhomogeneity of the geological formation as fractures andbedding.

FIGS. 4 and 5 schematically show parts of the electronic arrangement 3.The electronic arrangement 3 comprises a transmitter module 3′ and areceiver module 3″. Advantageously, the electronic arrangement 3 has anhomodyne electronics architecture, i.e. the transmitter module 3′ andthe receiver module 3″ are both coupled to a common high frequencysource LOS. The homodyne electronics architecture combined with theproximity of electronic arrangement to the transmitting and receivingantennas enables a reliable measurement of phase shift and amplitudeattenuation in the geological formation by eliminating systematic errorand noise sources.

The high frequency source LOS may be a dielectric resonator oscillatoror a coaxial resonator oscillator. The frequency of the high frequencysource LOS is variable and may be controlled via an appropriatecontrolling circuit, both device being well known in the art and thuswill not be further described.

The usual and known energizing and control circuits are omitted in theseFigures. The transmitter module 3′ is arranged to excite thetransmitting antennas 4A or 4B by applying an excitation signal ES.

The receiver module 3″ is arranged to determine an attenuation and aphase shift of a reception signal RS provided by a receiving antenna 5A,5B, 5C, 5D, 5E, 5F, 5G or 5H relatively to the excitation signal ES.

FIG. 4 schematically shows the transmitter module 3′. The transmittermodule 3′ comprises a first low frequency source LF1, a first modulatorMO1, a 90° phase-shifter PS90, a second low frequency source LF2, asecond modulator MO2, a splitter SP, a first amplifier A1 and a switchSW.

The high frequency source LOS is coupled to the first modulator MO1 andto the second modulator MO1 via the 90° phase-shifter PS90. It providesto these elements a microwave signal of high frequency ω_(o). The highfrequency may vary from around 10 MHz to around 2 GHz. The first lowfrequency source LF1 is coupled to the first modulator MO1. The secondlow frequency source LF2 is coupled to the second modulator MO2.

The modulator MO1 provides an in-phase signal IIS modulated with alow-frequency signal QΩ₁ (a few kHz—for example 15 kHz).

The 90° phase-shifter PS90 coupled to the modulator MO2 provides aquadrature signal QIS that is a 90° phase-shifted signal modulated withanother low-frequency signal Ω₂ (a few kHz—for example 10 kHz).

The low-frequency signals Ω₁ and Ω₂ may be chosen so as to eliminatedistortion in the signal due to any direct current bias andlow-frequency components noise in the source and in the modulators andalso to be compatible with digital processing electronic.

The in-phase IIS signal and quadrature signal QIS are summed into asplitter SP and amplified by the power amplifier Al. The resultingexcitation signal ES is then applied through a switch SW to either thevertical antenna element 44 or the horizontal antenna element 46 of thetransmitting antenna 4A or 4B. Advantageously, the switch SW multiplexesthe excitation signal ES to each antenna element in a sequential manner.The use of one transmitter module 3′ associated with the switch isadvantageous because any error (e.g. due to phase-shifter) will becommon for all the transmissions. The switch SW may be coupled to thetransmitting antenna 4A or 4B through a passive network (not shown) formatching impedance purpose. Alternatively, it is also possible toreplace the transmitter module associated with the switch with fourtransmitter modules without any switch, each one being coupled to anantenna element 44 or 46 of the transmitting antenna 4A or 4B.

FIG. 5 schematically shows the receiver module 3″. The receiver module3″ comprises a second amplifier A2, a mixer MX and a digitizing andprocessing module IQM.

The high frequency source LOS serves as a reference for the receivermodule 3″, in particular the mixer MX.

A receiving antenna R1 is coupled to the second amplifier A2, forexample a low noise amplifier. The receiving antenna R1 provides areception signal RS that is attenuated and phase-shifted relatively tothe excitation signal ES. The reception signal RS is amplified and theresulting amplified excitation signal is provided to the mixer MIX.

The mixer MIX which also receives the signal of high frequency ω_(o) ofthe high frequency source LOS demodulates the reception signal RS. Themixer MIX provides to the digitizing and processing module IQM a signalof low frequency Acos((φ)sin(Ω₁t)−Asin((φ)sin(Ω₂t). The digitizing andprocessing module IQM processes the signal and performs a synchronousdetection in order to extract the in-phase component of low frequency Ω₁and the quadrature component of low frequency Ω₂. The digitizing andprocessing module IQM provides the amplitude A and the phase φ of thereception signal.

Each antenna element 44 and 46 of each receiving antenna R1 is coupledto a receiver module 3″. The receiving antenna R1 refers to thereceiving antenna 5A, 5B, 5C, 5D, 5E, 5F, 5G and 5H which means that, inthe electromagnetic probe example of FIGS. 2, the electronic arrangement3 comprises sixteen receiver modules 3″ identical to the onehereinbefore described.

Alternatively, it is possible to replace the sixteen receiver modules 3″by a single receiver module. The single receiver module is coupled toall the receiving antennas by an appropriate switching element adaptedto perform multiplexing (e.g. Time Domain Multiplexing technique).

Advantageously, the paths between the various electronic components andthe antennas within the probe are well defined so that the phase delaysare well defined and phases of the reception signals can be comparedwithout error to the excitation signal.

Further, the gain and phase offset due to the high-frequency electronicschain that may affect the measurements can be cancelled with anappropriate calibration process during manufacturing process and anappropriate software correction at the probe level.

Advantageously, the high frequency source LOS is able to provide anexcitation signal comprising a plurality of frequencies. This enables anexcitation of the transmitting antenna according to a plurality offrequencies in a simultaneous manner. For example, a square waveformsignal could be used for its harmonic content. Accordingly, all thedesired frequencies are sent simultaneously into the geologicalformation and into the receiver circuit for simultaneous demodulation.

FIG. 6 schematically shows an open ended coaxial wire controllingcircuit 3″′ of the electronic arrangement 3 of the probe according tothe invention. The controlling circuit 3″′ comprises a transmittingmodule T3″′ and a receiving module R3″′. The transmitting module T3″′and the receiving module R3″′ are both coupled to a common highfrequency source LOS. The controlling circuit 3″′ is coupled to thefirst open-ended coaxial wire 6A. The usual and known energizing andcontrol circuits are omitted in this Figure.

The transmitting module T3″′ comprises a third low frequency source LF3,a third modulator MO3 and a directional coupler DCO. The receivingmodule R3″′ comprises the directional coupler DCO, a third amplifier A3,a second mixer MX2, and a second digitizing and processing module IQM2.

The high frequency source LOS is coupled to the modulator MO3 and to thesecond mixer MX2. The high frequency source LOS provides to theseelements a microwave signal of high frequency (ω_(o). The high frequencymay vary from around 10 MHz to around 2 GHz.

The third low frequency source LF3 is coupled to the third modulatorMO3. The modulator M03 provides an input signal IS modulated with alow-frequency signal Ω₃ (a few kHz—for example 20 kHz) in phase and inquadrature. The resulting input signal IS having a frequency ω_(o)+Ω₃ isprovided to the directional coupler DCO. The directional coupler DCOprovides the input signal IS to the open-ended coaxial wire 6A.

The high frequency source LOS serves as a reference for the receivingmodule R3″′, in particular the second mixer MX2.

The directional coupler DCO is also coupled to the third amplifier A3.The directional coupler DCO provides the output signal OS reflected bythe open-ended coaxial wire 6A. The output signal OS is amplified by theamplifier A3. The resulting amplified output signal having a frequencyω_(o)+Ω₃ is provided to the second mixer MX2. The mixer MIX2 which alsoreceives the signal of high frequency ω_(o) of the high frequency sourceLOS demodulates the output signal OS. The mixer MIX2 provides to thesecond digitizing and processing module IQM2 a signal of low frequencyunder the form A.cos(ωt+φ). The digitizing and processing module IQM2processes the signal, extracts the measured amplitude A′ and phase (φ′of the output signal and determines the complex reflection coefficientS11.

The gain and phase offset due to the high-frequency electronics chainthat may affect the measurements, can be cancelled with an appropriatecalibration process.

A sensibly identical controlling circuit is coupled to the secondopen-ended coaxial wire 6B and will therefore not be further described.

The electromagnetic probe according to the invention operates asdescribed hereinafter.

The electromagnetic probe enables to perform water saturation andconductivity radial profile in a limited zone surrounding the well-borehole (up to 4 inchs) in the horizontal and in the vertical directions.These measurements are performed at multiple depth of investigation andat multiple frequencies (e.g. ranging from 10 MHz to 2 GHz). Thesemeasurements enable to consolidate the petrophysical interpretation.

Each transmitting antenna and receiving antenna having two polarization(broadside and endfire), the electromagnetic probe enables anisotropymeasurements. The open-ended coaxial wires of the electromagnetic probeenable additional measurements. These additional measurements relate tothe mudcake properties and to the fluid mixture present in the bore holeand in the invaded zone.

Transmitters-receivers Measurements

The transmitting and receiving antennas are used to measure attenuationsand phase shifts of electromagnetic wave transmitted into the geologicalformation and reflected and/or refracted by the geological formation. Asthe antennas are sensibly pure magnetic point dipole, a simple inversionenables to retrieve the apparent wave vector k. It is well known by aperson skilled in the art that the wave vector k is directly linked tothe permittivity and conductivity of the geological formation (this willnot be further described).

The architecture of the transmitting antennas and receiving antennas inthe pad enables to implement a borehole compensation scheme. This schemeis exploited to both eliminate the acquisition systematic andconcentrate the measurement spatial response between the twotransmitting antennas. The borehole compensation scheme results in fourgeometrical measurement elements, each of them corresponding to acompensated two-transmitters-receiver spacing. The four elements providefour measurements corresponding to different radial depths RD₁, RD₂, RD₃and RD₁ (see FIG. 2.A).

The electromagnetic probe offers two magnetic dipole polarizations: theendfire polarization EF, and the broadside polarization BS. All thepossible configurations for the various transmitter-receiver dipoleassociations can be measured. The mixed transmitter-receiver dipoleassociations EF-BS and BS-EF enable to perform cross-dipolemeasurements. The collinear transmitter-receiver dipole associationsEF-EF and BS-BS enable to perform parallel-dipole measurements. Theparallel-dipole and cross-dipole measurements provide different type ofinformation.

FIG. 7.A illustrates typical envelopes of the radial measurementsensitivity response for transmitting antenna/receiving antennaaccording to the endfire mode for the radial investigation depths RD1,RD2, RD3 and RD4. This graph illustrates that the EF-EF radial responsefor a given measurement element is concentrated around its radial depthof investigation.

FIG. 7.B illustrates typical envelopes of the radial measurementsensitivity response for transmitting antenna/receiving antennaaccording to the broadside mode for the radial investigation depths RD1,RD2, RD3 and RD4. This graph illustrates that the BS-BS radial depth ofinvestigation has a significant contribution in the shallow region. Theresulting radial depth of investigation is shallower than the EF-EFmeasurement.

The electric field of the endfire EF polarized antennas in homogeneousformation stands in the depth transverse plane. Hence, the EF-EFmeasurement is only sensitive to transverse formation properties, whilethe BS-BS measurement is sensitive to transverse and parallel formationproperties. Using both measurements allows separating the transverse andparallel properties of the formation, and hence measuring the formationanisotropy.

The cross-dipole measurements are non-zero when the formation isanisotropic or inhomogeneous. These measurements are used to consolidatethe anisotropy measurement and to characterize the presence of bed dipwithin the geological formation. The depth of investigation of the crossdipole is of the broadside BS type, concentrated around the broadside BSpolarized antennas; hence the BS-EF and EF-BS measurements are notequivalent.

Open-ended Coaxial Wires Measurements

The first open ended coaxial wire is in contact with the mud-cake orwith the formation. The second open ended coaxial wire is exposed to thebore hole fluid mixture. The first open ended coaxial wire is operatedin two ways: as standalone reflection antenna, as propagating receiverantenna when associated with the transmitting antennas, and finally astransmitter when coupled with the closest cross-dipole receivers. Thesecond open ended coaxial wire is operated as standalone reflectionantenna only.

In reflection mode, a microwave signal is sent to the open-ended coaxialwire aperture into the geological formation, the mudcake or the fluidmixture, and the reflected signal attenuation and phase shift ismeasured. The complex reflection coefficient generally known in the artas S11 is determined based on the measured attenuation and phase shift.The open-ended coaxial wires depth of investigation is shallow. Thedepth of investigation corresponds to the coaxial wire transversesection, for example around 1 mm for a 2 mm diameter wire. Consequently,the complex reflection coefficient S11 is only linked to the mudcake orthe fluid mixture dielectric properties. A simple linear inversionprocess provides the permittivity and conductivity of the mudcake and/orthe fluid mixture.

The open-ended coaxial wires may also be used in propagation mode. Inthis case, the open-ended coaxial wire is sensibly a pure electricdipole perpendicular to the first surface of the pad. Thecavity-antennas being assimilated to magnetic dipoles, a transmissionmeasurement with a simple forward model is hence possible. The signaldelivered by the coaxial wire in transmission mode will be proportionalto the normal electric field at its aperture.

The first open ended coaxial wire operating in reflection mode is usedto indicate the eventual presence of mud-cake and to determine themud-cake electromagnetic properties. It also enables to deliver anindication of the pad contact quality/efficiency. The first open endedcoaxial wire operating in propagation mode is used, when associated withthe transmitting antenna operating in broadside mode, to provide anon-zero measurement with an increased radial depth when compared to thereflection mode. This measurement is an additional shallow measurementthat completes the magnetic dipole radial responses.

The second open ended coaxial wire is used to characterize the bore holefluid mixture electromagnetic properties.

Measurements Summary

Therefore, various sets of measurements relating to the geologicalformation are possible with the electromagnetic probe:

-   measurements through the cavity antennas sensibly corresponding to    pure magnetic dipoles tangential to the pad plane,-   measurements through the first open-ended coaxial wire sensibly    corresponding to pure electric dipole normal to the pad, the coaxial    wire working in transmission, in reflection and in reception modes,-   measurements according to different polarizations,-   measurements according to different radial depths, and-   measurements according to different frequencies.

Measurements performed by means of the first open-ended coaxial wire andthe eight parallel-dipole, when the transmitting antennas operate inbroadside mode and in endfire mode, enable to determine the mudcakethickness and geological formation electromagnetic properties,anisotropy, and radial profile.

Measurements performed by means of the first open-ended coaxial wire andthe eight cross-dipole, when the transmitting antennas operate inbroadside mode and in endfire mode, enables to determine the anisotropy,dip and fractures quantifications and orientation of the geologicalformation.

The above measurements are performed at different frequencies. Theelectromagnetic properties variations with frequency enable to determineadditional petrophysic parameters. For example, FIG. 8.A shows typicaldispersion curve relatively to the frequency of the permittivity ofwater filled porous rock. FIG. 8.B shows typical dispersion curverelatively to the frequency of the conductivity of water filled porousrock.

Moreover, additional sets of measurements relating to the mudcake and/orto the fluid mixture electromagnetic properties may be performed withthe electromagnetic probe by means of the first and second open-endedcoaxial wires working in reflection. The additional sets of measurementsmay also be performed according to different frequencies.

After reconciling the radial investigation depth at differentfrequencies, a radial characterization of the geological formation ispossible.

Finally, assuming the fluid mixture electromagnetic properties areknown, it is possible to identify the fractures orientations within thegeological formation. The fractures may be natural fractures due to thegeological formation stress or fractures induced by the drillingoperation. The fractures may be filled with the fluid mixture from thebore hole (generally conductive because enriched in water) or withhydrocarbon fluid mixture (generally resistive).

If a fracture is parallel to the pad axis, a resistive fluid filledfracture will create a sensibly zero signal according to the broadsidemode and an important signal according to the endfire mode.

If a fracture is perpendicular to the pad axis, a resistive fluid filledfracture will create an important signal according to the broadside modeand a sensibly zero signal according to the endfire mode.

If a fracture is tilted relatively to the pad axis, a resistive fluidfilled fracture will create a signal being a combination of thebroadside mode and the endfire mode.

Final Remarks

A particular application of the invention relating to a wireline toolhas been described. However, it is apparent for a person skilled in theart that the invention is also applicable to a logging-while-drillingtool. A typical logging-while-drilling tool is incorporated into abottom hole assembly attached to the end of a drill swing with a drillbit attached at the extreme end thereof. Measurements can be made eitherwhen the drill string is stationary or rotating. In the latter case anadditional measurement is made to allow the measurements to be relatedto the rotational position of the drill string in the bore hole. This ispreferably done by making simultaneous measurements of the direction ofthe earth's magnetic field with a compass which can be related to areference measurement made when the drill string is stationary. It willalso be apparent for a man skilled in the art that the invention isapplicable to onshore and offshore hydrocarbon well location.

It is apparent that the term “pad” used hereinbefore genericallyindicates a contacting element with the surface of the bore hole wall.The particular contacting element shown in the Figures for maintainingthe antennas in engagement with the bore hole wall is illustrative andit will be apparent for a man skilled in the art that other suitablecontacting element may be implemented, for example a sonde with a backuparm.

The same remark is also applicable to the particular probe deployingsystem shown on the Figures.

Finally, it is also apparent for a person skilled in the art thatapplication of the invention to the oilfield industry is not limitativeas the invention can also be used in others types of geological surveys.

The drawings and their description hereinbefore illustrate rather thanlimit the invention.

Any reference sign in a claim should not be construed as limiting theclaim. The word “comprising” does not exclude the presence of otherelements than those listed in a claim. The word “a” or “an” preceding anelement does not exclude the presence of a plurality of such element.

1. An electromagnetic probe (1) for measuring the electromagneticproperties of a subsurface formation (GF) in a limited zone surroundinga well-bore hole (WBH), the well-bore hole being filled with a well-borefluid (DM), the probe comprises: a pad (2) having a first face defininga first area arranged to be positioned in contact with a well-bore wall(WBW), wherein the probe (1) further comprises: at least twotransmitting antennas (4A, 4B) defining a central point (CP) betweenthem, each antenna being spaced from a distance (d₀) from the centralpoint, at least a first (5A, 5B) and a second set (5C, 5D) of receivingantennas, each set comprising a first receiving antenna (5A; 5C) and asecond receiving antenna (5B; 5D), the first receiving antenna beingpositioned on one side of the transmitting antennas and the secondreceiving antenna being positioned on other side of the transmittingantennas so that each set encompass the transmitting antennas (4A, 4B).the first set of receiving antennas (5A, 5B) is spaced from a firstdistance (d₁) from the central point (CP), the second set of receivingantennas (5C, 5D) is spaced from a second distance (d₂) from the centralpoint (CP), the second distance (d₂) being greater than the firstdistance (d₁), the transmitting (4A, 4B) and receiving (5A, 5B, 5C, 5D)antennas are positioned along a line (AA′) in the first face, and anelectronic arrangement (3) comprising at least one transmitter module(3′) arranged to excite the transmitting antennas (4A, 4B) by applyingan excitation signal according to at least a first and a secondfrequency, and at least one receiver module (3″) coupled to at least onereceiving antenna (5A; 5B; 5C; 5D) and arranged to determine anattenuation and a phase shift of each reception signal provided by eachreceiving antenna (5A; 5B; 5C; 5D) relatively to the excitation signal.2. A probe for measuring the electromagnetic properties of a subsurfaceformation according to claim 1 wherein the transmitting antennas (4A,4B) are sensibly identical, each antenna (4A; 4B) comprising twoperpendicular dipoles (44, 46) embedded in a cavity (42) and arranged totransmit electromagnetic energy according to a broadside mode (BSM) andan endfire mode (EFM).
 3. A probe for measuring the electromagneticproperties of a subsurface formation according to claim 1, wherein thereceiving antennas (5A, 5B, 5C, 5D) are sensibly identical, each antenna(5A; 5B; 5C; 5D) comprising two perpendicular dipoles (44, 46) embeddedin a cavity (42) and arranged to receive electromagnetic energyaccording to a broadside mode (BSM) and an endfire mode (EFM).
 4. Aprobe for measuring the electromagnetic properties of a subsurfaceformation according to claims 1, wherein the probe further comprises afirst open-ended coaxial wire (6A) arranged in the first side andpositioned sensibly perpendicularly to the first area between atransmitting antenna (4A) and a receiving antenna (5B).
 5. A probe formeasuring the electromagnetic properties of a subsurface formationaccording to claim 4, wherein the electronic arrangement (3) furthercomprises a first open ended coaxial wire controlling circuit (3′″),said circuit comprising: a transmitting module (T3′″) for sending ahigh-frequency input signal (IS) into the first open ended coaxial wire(6A), and a receiving module (R3′″) for determining a first reflectioncoefficient based on a high frequency output signal (OS) reflected bythe first open-ended coaxial wire and a propagation coefficient based ona high frequency output signal (OS) received by tile first open-endedcoaxial Wire following an excitation of the transmitting antennas (4A,4B).
 6. A probe for measuring the electromagnetic properties of asubsurface formation according to claim 1, wherein the pad (2) furthercomprises a second face arranged to be in contact with the well-borefluid (DM), and the probe (1) further comprises a second open-endedcoaxial wire (6B) arranged in the second face.
 7. A probe for measuringthe electromagnetic properties of a subsurface formation according toclaim 6, wherein the electronic arrangement further comprises a secondopen ended coaxial wire controlling circuit (3′″), said circuitcomprising: a transmitting module (T3″′) for sending a high-frequencyinput signal (IS) into the second open ended coaxial wire (6B), and areceiving module (R3″′) for determining a second reflection coefficientbased on a high frequency output signal (OS) reflected by the secondopen-ended coaxial wire (6B).
 8. A probe for measuring theelectromagnetic properties of a subsurface formation according to claim1, wherein the electronic arrangement (3) has a homodyne architecturecomprising a variable high frequency source (LOS) providing a highfrequency signal to: the at least one transmitter module (3′) arrangedto excite the transmitting antennas (4A, 4B), the at least one receivermodule (3″) coupled to the at least one receiving antenna (5A; 5B; 5C;5D), and the transmitting, module (T3″′) and tile receiving module(R3″′) of the first and second open ended coaxial wire controllingcircuits (3′″).
 9. A logging tool (TL) arranged to be deployed in awell-bore hole (WBH), wherein the logging, tool (TL) comprises a probe(1) according to claim 1 and a positioning arrangement (AR) forpositioning the probe in contact with a well-bore wall (WBW) at adetermined depth in the well bore hole (WBH).
 10. A method for measuringthe electromagnetic properties of a subsurface formation (GF) in alimited zone surrounding a well-bore hole (WBH), the well-bore holebeing filled with a well-bore fluid (DM), the method comprises the stepsof: a) positioning a probe (1) for measuring the electromagneticproperties of the subsurface formation in contact with a well-bore wall(WBW) at a first depth, the probe comprising at least two transmittingantenna (4A, 4B) and at least a first (5A, 5B) and a second (5C, 5D) setof receiving antennas, wherein the method further comprises the stepsof: b) transmitting an excitation electromagnetic energy around acentral point (CP) into the limited zone by energizing at firsttransmitting antenna (4A, 4B) with an excitation signal (ES) accordingto a broadside mode (BSM) and according to a first frequency, c)measuring a broadside/broadside reception signal (RS) at the receivingantennas (5A. 5B, 5C, 5D) according to a broadside mode (BSM) andmeasuring simultaneously a broadside/endfire reception signal (RS) atthe receiving antennas (5A, 5B, 5C, 5D) according to an endfire mode(EFM), at least at a first distance (d₁) and at a second distance (d₂)from the central point (CP), d) repeating the transmitting step b) andthe measuring steps c) by energizing a second transmitting antenna (4B;4A) with an excitation signal (ES) according to a broadside mode (BSM)and according to a first frequency, e) transmitting an excitationelectromagnetic energy around a central point (CP) into the limited zoneby energizing the first transmitting antenna (4A; 4B) with an excitationsignal (ES) according to an endfire mode (EFM) and according to thefirst frequency. f) measuring an endfire/broadside reception signal (RS)at the receiving antennas (5A, 5B, 5C 5D) according to the broadsidemode (BSM) and measuring simultaneously a broadside/endfire receptionsignal at the receiving antennas (5A, 5B, 5C 5D) according to theendfire mode (EFM) at least at the first distance (d₁) and at a seconddistance (d₂) from the central point (CP), g) repeating the transmittingstep e) and the measuring steps f) by energizing the second transmittingantenna (4B; 4A) with an excitation signal (ES) according to a endfiremode (EFM) and according to a first frequency and h) repeating thetransmitting and measuring steps b) to g) at least at a secondfrequency.
 11. A method for measuring the electromagnetic properties ofa subsurface formation according to claim 10, wherein the transmittingsteps b), d), e) and g) are performed simultaneously, the excitationelectromagnetic energy transmitted by the first transmitting antennasbeing signed by a first low frequency, the excitation electromagneticenergy transmitted by the second transmitting antennas being signed by asecond low frequency.
 12. A method for measuring the electromagneticproperties of a subsurface formation according to claim 10, wherein thetransmitting steps b) to h) are performed simultaneously, the excitationsignal (ES) comprising a plurality of frequencies at least the first andthe second frequencies.
 13. A method for measuring the electromagneticproperties of a subsurface formation according to any one of the claim10, wherein the method further comprises the steps of: determining anattenuation and a phase shift of each reception signal (RS) provided byeach receiving antenna (5A, 5B, 5C, 5D) relatively to the excitationsignal (ES), estimating the electromagnetic properties of the subsurfaceformation at different frequencies in the limited zone surrounding thewell-bore hole (WBH) for at least a first radial investigation depth(RD₁) correlated to the first distance (d₁) and a second radialinvestigation depth (RD₂) correlated to the second distance (d₂).
 14. Amethod for measuring the electromagnetic properties of a subsurfaceformation according to claim 10, wherein the method further comprisesthe steps of: measuring a high frequency output signal (OS) received bya first open-ended coaxial wire (6A) following an excitation of thetransmitting antennas (4A, 4B), determining, an attenuation and a phaseshift of the high frequency output signal (OS) relatively to theexcitation signal (ES), and estimating a thickness of a mudcake (MC) onthe well-bore wall (WBW) by determining a transmission coefficient basedon the attenuation and phase shift.
 15. A method for measuring theelectromagnetic properties of a subsurface formation according to claim10, wherein the method further comprises the steps of: measuring a highfrequency output signal (OS) received by the receiving antennas (5B, 5D)following an excitation of a first open-ended coaxial wire (6A),determining an attenuation and a phase shift of the high frequencyoutput signal (OS) relative to the excitation signal (ES), andestimating a thickness of a mudcake (MC) on the well-bore wall (WBW) bydetermining a propagation coefficient based on the attenuation.
 16. Amethod for measuring the electromagnetic properties of a subsurfaceformation according to claim 10, wherein the method further comprisesthe steps of: sending a high-frequency input signal (IS) into a firstopen ended coaxial wire (6A) in contact with the well-bore wall (WBW),measuring a high frequency output signal (OS) reflected by the firstopen-ended coaxial wire estimating the electromagnetic properties of themudcake (MC) on the well-bore wall (WBW) by determining a mudcakereflection coefficient based on the high frequency output signal (OS).17. A method for measuring the electromagnetic properties of asubsurface formation according to claim 10, wherein the method furthercomprises the steps of: sending a high-frequency input signal (IS) intoa second open ended coaxial wire (6B) in contact with a well-bore fluid(DM), measuring a high frequency output signal (OS) reflected by thesecond open-ended coaxial wire (6B), and estimating the electromagneticproperties of the well-bore fluid by determining a well-bore fluidreflection coefficient based on the high frequency output signal (OS).18. A method for measuring the electromagnetic properties of asubsurface formation according to claim 10, wherein the method furthercomprises the step of correcting the calculated electromagneticproperties of the subsurface formation (GF) in the limited zonesurrounding the well-bore hole (WBH) based on the estimatedelectromagnetic properties and the thickness of the mudcake (MC).
 19. Amethod for measuring the electromagnetic properties of a subsurfaceformation according to claim 10, wherein the method further comprisesthe step of comparing the signals provided by the first open endedcoaxial wire and the second open ended coaxial wire for estimating thequality of the pad (2) application against the bore-hole wall (WBW).